Since relative trisections with non-empty binding (\(b>0\) ) satisfy the conditions of Lemma REF , our result extends the gluing theorems of [1]} and [2]}. In this case (\(b>0\) ), the monodromy algorithm of [3]} is helpful to find the image of the filling arcs under \(f\) .
In general, in order to glue two \(\star \) -trisections with Theorem REF , one might need to poke the given diagrams (see Subsection REF ) enough times to ensure that every connected component \(\partial _- (W_i\cap W_j)\)  is a surface with boundary. In particular, for relative trisections with \(b=0\) , it is sufficient to poke the trisection surface three times.
